How will Rand Paul, other Senate GOP newcomers fit in?

Even as he celebrated winning Kentucky's U.S. Senate race Tuesday night, tea party-backed Republican Rand Paul sketched out the next big question.

"We came from nowhere and won a big victory. Now we have to see if we can do something with the victory," Paul said.

Senate Minority Leader Mitch McConnell, Kentucky's senior senator, in large measure holds the answer to that question for Paul and other maverick Senate newcomers.

It will be interesting to see the dynamics between McConnell, a master of the establishment GOP, and Paul and others who won election by throwing rocks at that establishment, analysts said.

There is a fight for the soul of the party, said Jasmine Farrier, a political science professor at the University of Louisville.

"I see a lot of tension here. They either co-opt the tea party or the tea party co-opts them," Farrier said of the Republican establishment. "Neither of those things will be easy."

Paul believes the tea party message is winning.

"We're shaping the debate and the party is coming in our direction, I think," he said during a campaign stop Monday.

In an interview with CNN the next morning, Paul said that although he will agree with McConnell in many areas, "We will challenge him from day to day."

And when he won that night, Paul made clear he intends to try to rattle the cage in Washington, listing a litany of issues he will ask the Senate to consider, including why citizens have to balance their budgets but Congress doesn't. Another signature piece of Paul's campaign was a Constitutional amendment requiring a balanced federal budget.

Republicans gained several Senate seats Tuesday, narrowing the gap with Democrats and giving McConnell more power.

Even if some of the newcomers don't want to cooperate with McConnell, he will have enough members to frustrate the Democratic majority, analysts said.

But if some of those extra bodies are not team players, there still could be some problems, said Stuart Rothenberg, publisher of The Rothenberg Political Report.

However, Rothenberg noted that several candidates who lost would have bulked up a tea party caucus in the Senate, including Sharron Angle in Nevada and Christine O'Donnell in Delaware, while others appear endangered as vote-counting continues, such as Joe Miller in Alaska.

"In some ways, Mitch is lucky that some of the troublemakers lost, or seem to be losing," Rothenberg said.

The tea party-backed candidates who did win will be eager to prove to their base that they won't be co-opted by the Beltway establishment, said Larry Sabato, director of the Center for Politics at the University of Virginia.

"You can expect some dust-ups on that basis alone," he said. " McConnell will have to work hard to keep the tea party senators inside the tent."That may mean keeping close contact with Sen. Jim DeMint of South Carolina, the current chief Senate ally of the tea party, even though DeMint is not terribly popular with colleagues right now, Sabato said.

Farrier noted that the Senate's rules give the minority, and individual lawmakers, a variety of effective avenues to stop legislation.

That means Paul could hold up legislation in order to highlight his message — as Kentucky's current junior senator, Republican Jim Bunning, did earlier this year when he briefly stalled extended unemployment benefits to protest deficit spending.

"I don't see a lot of go along to get along" from Paul, Farrier said.

However, Jennifer Duffy, a senior editor at the Cook Political Report, said McConnell has the upper hand in dealing with the newcomers because of his position and the way the chamber operates.

"Some of the new members who don't know how the legislative body works might be in for a rude awakening. I would put Rand Paul at the top of that list," Duffy said. "He might not think he needs McConnell but he needs McConnell more than McConnell needs him."

In a conference call Wednesday, McConnell laughed off a question about Paul challenging him, saying that wouldn't make the junior senator different than any other Senate Republican.

McConnell predicted he and Paul will have a good relationship.

"I think we're going to have a high level of unity" in the GOP caucus, he said.

The members won't agree on everything, McConnell said, but they share a common view that government has spent and borrowed too much the last two years and needs to cut back.

That's clearly the message voters sent Tuesday, McConnell said.

Even though the GOP made big gains, McConnell said the election "was not an endorsement of us, it was a repudiation of what the other side has been doing."

McConnell said one key goal is to repeal the health care reform law Congress approved this year.

There will be a vote on repeal, and if that doesn't work, Republicans will try to wipe out specific parts, such as the mandate for people to buy insurance or pay a penalty.

However, McConnell also cited several areas where he said Republicans can work with President Barack Obama, including trade agreements and nuclear energy.